1. Field of the Invention
The present invention relates to a method for determining consistent water relative permeability values (k.sub.rw) from dynamic displacement measurements conducted on a subsurface core sample.
2. Discussion of the Prior Art
Water and oil relative permeability values are used in a number of significant ways in many water and oil reservoir engineering calculations. However, it is different to measure water and oil relative permeabilities in the laboratory on a core sample. Two techniques are typically used by the oil industry to obtain water and oil relative permeability values. The first is the so-called steady state method, which is described in the article entitled "Relative Permeability Measurements on Small Core Samples" by Morris, R. H. et al, The Procedures Monthly, pp. 19-25, August, 1947. The other method is the dynamic displacement method, which is described in the following articles: "A Simplified Method for Computing Oil Recovery by Gas or Water Drive" by Wedge, H. J., Transactions, AIME, Vol. 195, pp. 91-98, 1952; "Calculation of Relative Permeability From Displacement Experiments" by Johnson, E. F. et al, Transactions, AIME, Vol. 216, pp. 370-372, 1959; "Graphical Techniques for Determining Relative Permeability From Displacement Experiments" by Jones, S. C. et al, Transactions, AIME, Vol. 265, PP. 807-817, 1978. This latter article discloses a graphical technique for determining relative oil (k.sub.ro) and water (k.sub.rw) permeability values from dynamic displacement measurements, which technique will be hereinafter referred to as the Jones and Roszelle technique.
A significant problem with using a steady state technique to determine water relative permeability values is that it is time consuming, as the steady state measurements required take considerable time for stabilization. Thus, a few days may be required for every data point of a plot of water relative permeability vs. core saturation (water (S.sub.w) or oil (S.sub.o)) which is calculated in the technique and thus weeks are required to obtain a complete water relative permeability curve.
In the dynamic displacement method of calculating water relative permeability values, a small core sample is flooded with water to saturation and then flooded with oil to its irreducible water saturation. This cycle is repeated while the pressure drop across the core, and the oil and water production fractions, as a function of total oil and water injected (injection rate x time), are recorded. This data, together with oil and water viscosity, the absolute permeability of the core, and the core pore volume, are used to calculate oil relative permeability values (k.sub.ro), as well as water relative permeability values (k.sub.rw), as a function of saturation (oil or water) at the effluent end of the core. A greater appreciation of this conventional technique can be had by review of those above-referenced articles which discuss the dynamic displacement method.
The theory upon which interpretation of the dynamic displacement data rests and upon which water relative permeability determinations are made assumes that the capillary pressure effects on the core saturation distribution are negligible. However, there is an observable pressure drop discontinuity near the effluent end of the core sample causd by capillary forces, which is known as the "end-effect". This resistance to effluent flow distorts the pressure drop data which are taken during a dynamic displacement test, causing consequent distortions in both relative oil and water permeability values determined from that data.
The so-called "end-effect" was perhaps first recognized by Richardson, et al and reported in the article entitled "Laboratory Determination of Relative Permeability", Richardson, J. G. et al, Transactions, AIME, Vol. 195, pp. 187-196; 1952. In this article, Richardson, et al report experimental results of a two-phase flow on a 30 centimeter long core sampler cut into 8 sections. The sections were arranged perpendicular to the axis of the core and were machined and clamped together in a flow apparatus. Two-phase flow experiments were run at various flow rates and the saturaton in each section was measured for each experiment. The results show that near the outflow or effluent end of a core sample, a zone exists where the wetting phase saturation increases rapidly and achieves a maximum value at the effluent face. Beyond this zone, towards the inflow end, the saturation is uniform. The width of the zone decreases with an increase in flow rate.
It appears from the results reported by Richardson, et al that a very high flow rate is required in the dynamic displacement tests to effectively remove the end zone and its effects on the dynamic displacement data used for determining relative water permeability values. However, physical limitations on the experimental equipment used in the dynamic displacement measurements typically do not permit the high rates of flow which would be required to eliminate measurement perturbations caused by the end-effect. Moreover, it is difficult to determine a critical minimum flow rate which is required to eliminate these perturbations.